The official language of Bhutan is Dzongkha (pronounced dz-ong-ka) , a confusing, hard-to-learn, interesting.. etc. language. Some people, especially in rural places, have a difficulty or even don't know how to speak Dzongkha. In the provincial lands, some common languages are Sharshop (often also called Sharshogpa), and Nepali. In Bumthang, Bumthap is spoken. There are many, many, many kinds of languages in Bhutan, and now in Thimphu most schools teach in English, Dzongkha as a second language.
Hindi and other Indian languages are not too uncommon, too. But don't worry! People, especially in Thimphu, will have a good vocabulary of English, and if you are from other nations, Bhutanese guides with knowledge of different languages like Spanish, Japanese, German, French, Chinese and other strange and wide-spread languages are being paid 100$ a day!
If a urgent desire urges you to learn Dzongkha, then Bhutanese friends are just the people to teach you, so come on - it isn't as complicated as it looks (well, kind of).